You're stargazing on a dark night, and you spot a satellite moving across the sky at an angle of elevation of 20 degrees. If the satellite is 800 kilometers away from you, calculate its altitude.
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To calculate the satellite's altitude, we can use trigonometry.
The angle of elevation is the angle between the horizontal line and the line connecting the observer to the satellite. We can consider this angle as the angle in a right-angled triangle, where the hypotenuse is the distance from the observer to the satellite, and the opposite side is the altitude.
The opposite side represents the altitude, and the hypotenuse represents the distance between the observer and the satellite, which is 800 kilometers.
Now we can use the sine function to determine the altitude:
sin(angle) = opposite / hypotenuse
Plugging in the values:
sin(20°) = altitude / 800
Rearranging the formula to solve for the altitude:
altitude = sin(20°) * 800
Calculating this:
altitude ≈ 273.25 kilometers
Therefore, the satellite's altitude is approximately 273.25 kilometers.
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